2 problems

Let $\mathcal{H}$ be a simple $3$-partite $3$-graph with vertex classes $A$, $B$ and $C$. Suppose each vertex in $A$ has degree at least $r$, and each vertex in $B \cup C$ has degr…

Let $\mathcal{H}$ be an $r$-regular simple $3$-partite $3$-graph with $n$ vertices in each class. Aharoni–Kotlar–Ziv conjecture. … This conjecture concerns the matching number of s…